DIRECT VARIATION September 8 & 9, 2016 https://www.youtube.com/watch?v=WGqmAmzUODM.

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Presentation transcript:

DIRECT VARIATION September 8 & 9,

WHAT IS A DIRECT VARIATION? A direct variation is when two variables have a relationship in which one varies – changes – proportionally as the other changes. As one variable increases the other increases or as one variable decreases the other decreases.

REAL LIFE EXAMPLES The number of points scored by a soccer team is in direct proportion to the number of goals made. The profit of a movie is in direct proportion to the number of tickets sold. If you earn an hourly wage, the amount of money you earn is in direct proportion to the number of hours you work. The amount of time it takes to drive across the country is in direct proportion to the speed at which one travels.

Direct VariationInverse Variation A direct variation is expressed in the form y = kx with the slope defined by k, which is your constant of variation.

HOW DO I FIND “K”, THE “CONSTANT”? k = y = kx

WHAT IS THE CONSTANT OF VARIATION? The k in the direct variation formula is called the constant of variation. It tells you how much y will change as x changes. For instance, look at y = 2x, if k = 2, as x changes, y will change 2 times this value. So if x = 2 then y = 4, or if x = 3 then y = 6

DIRECT VARIATION PROBLEMS Given the ordered pair (3,9) write an equation of the direct variation. Step 1. Plug in your given information in the direct variation formula y=kx (plug in 3 for x and 9 for y) 9= k(3) Step 2. Divide both sides by 3 9/3 = k Step 3. k=3 Step 4. Now plug 3 into the formula y = kx y = 3x

WORD PROBLEM # 1 The Ford F-150 can travel 150 miles on 10 gallons of gas. How much gas is required to travel 750 miles?

WORD PROBLEM # 2 Drew gets paid hourly at his job. If Drew gets $50 dollars for a 5 hour shift, how much will he be paid for a 7 hour shift? Find k and write an equation to solve this question.